The polygenic model has been used in attempts to enhance selection efficacy in plant breeding programs. By observation and careful measurements of results of various parental-offspring distributions, both in plants and animals, and by expressing the genetic relationships in mathematical correlations, a complex mathematical theory emerged. See, e.g., Wright (1977) Evolution and the Genetics of Populations, vol. 5, University of Chicago Press, Chicago, Ill.
A basic tenant of this theory is the expression of phenotypic distribution in terms of its variance and dissection of that variance into its causative components. By studying the variance in offspring distributions where the offspring result from various types of crosses, and by determining the correlation between phenotypic distributions of different pedigree relationships (parent-offspring, offspring of the same cross, subsequent generations, e.g., F2-F3,) it was determined that the phenotypic variance (VP) had as basic components genotypic variance (VG) and environmental variance (VE). In a simple case, the variance of plants of the same genotype grown in different environments provides an estimate of the effects of environment. Factors contributing to the environmental variance include year of growth and differences in the soil composition of plots of land.
In turn, each of these components could be further subdivided, for example, by separating VG into additive (VA), dominance (VD) and epistatic (VI) components. The components of the variance could be estimated by breeding experiments. These values were then used to predict results of other breeding crosses. Response to selection was found to be a function of the heritability of the trait, the selection differential and the intensity of selection.
The heritability (h2) of a trait is broadly defined ash2=VG/VP,or more narrowly,  (1)h2=VA/VP  (2)and is a predictor of the degree to which values of traits may be transmitted from parents to offspring.
Advancement of hybrid and inbred lines are conducted based on large scale trials and through several statistical analysis methodologies. Lines are advanced for meeting specific criteria for grain yield, moisture content as well as certain key agronomics. The genetic evaluation of the different lines provides an estimate of the general combining abilities (GCA) of inbred lines (in other words, an evaluation of their value as parents of hybrids) as well as an estimate of the specific combining ability (SCA), reflecting the evaluation of the hybrid itself.
The goal of plant breeding in corn is to develop inbred parent lines that contribute various desirable traits to the hybrids in which they are used. These traits may include resistance to diseases and insects, tolerance to heat and drought, reducing the time to crop maturity, greater yield, and better agronomic quality. With mechanical harvesting of many crops, uniformity of plant characteristics such as germination and stand establishment, growth rate, stalk strength, root strength, ear retention, maturity, and plant and ear height, is important.
Field crops are bred through techniques that take advantage of the plant's method of pollination. A plant is self-pollinated if pollen from one flower is transferred to the same or another flower of the same plant. A plant is cross-pollinated if the pollen comes from a flower on a different plant.
Plants that have been self-pollinated and selected for type for many generations become homozygous at almost all gene loci and produce a uniform population of true breeding progeny. A cross between two homozygous lines produces a uniform population of hybrid plants that may be heterozygous for many gene loci. A cross of two plants each heterozygous at a number of gene loci will produce a population of hybrid plants that differ genetically and will not be uniform.
Corn plants (Zea mays L.) can be bred by both self-pollination and cross-pollination techniques. Corn has separate male and female flowers on the same plant, located on the tassel and the ear, respectively. Natural pollination occurs in corn when wind blows pollen from the tassels to the silks that protrude from the tops of the incipient ears.
The development of corn hybrids requires the development of homozygous inbred lines, the crossing of these lines, and the evaluation of the crosses. Pedigree breeding and recurrent selection breeding methods are used to develop inbred lines from breeding populations. Breeding programs combine the genetic backgrounds from two or more inbred lines or various other broad-based sources into breeding pools from which new inbred lines are developed by selfing and selection of desired phenotypes. The new inbreds are crossed with other inbred lines and the hybrids from these crosses are evaluated to determine which of those have commercial potential.
Pedigree breeding starts with the crossing of two genotypes, each of which may have one or more desirable characteristics that is lacking in the other or which complement the other. If the two original parents do not provide all of the desired characteristics, other sources can be included in the breeding population. In the pedigree method, superior plants are selfed and selected in successive generations. In the succeeding generations, the heterozygous condition gives way to homogeneous lines as a result of self-pollination and selection. Typically in the pedigree method of breeding, five or more generations of selfing and selection is practiced: F1; F2; F3; F4; F5, etc. These selfing generations are sometimes designated as S0, S1, S2, etc with S0 being an equivalent to F1 while S2 is an equivalent to F3, etc.
Backcrossing can be used to improve an inbred line or to develop a closely related new inbred line depending on the number of backcross generations and backcross methods employed. Backcrossing transfers a specific desirable trait from one inbred or source to an inbred that lacks that trait. This can be accomplished, for example, by first crossing a superior inbred (A) (recurrent parent) to a donor inbred (non-recurrent parent), which carries the appropriate gene(s) for the trait in question. The progeny of this cross is then mated back to the superior recurrent parent (A) followed by selection in the resultant progeny for the desired trait to be transferred from the nonrecurrent parent. After five or more backcross generations with selection for the desired trait, the progeny will be heterozygous for loci controlling the characteristic being transferred, but will be like the superior parent for most or almost all other genes. After the last backcross generation, the inbred line would be selfed to give pure breeding progeny for the gene(s) being transferred.
A single cross hybrid corn variety is the cross of two inbred parent lines, each of which has a genotype which complements the genotype of the other. The hybrid progeny of the first generation is designated F1. In the development of hybrids, only the F1 hybrid plants are sought. Preferred F1 hybrids are more vigorous than their inbred parents. This hybrid vigor, or heterosis, can be manifested in many polygenic traits, including increased vegetative growth and increased yield.
The development of a hybrid corn variety involves three steps: (1) the selection of plants from various germplasm pools; (2) the selfing of the selected plants for several generations to produce a series of inbred lines, which, although different from each other, breed true and are highly uniform; and (3) crossing the selected inbred lines with unrelated inbred lines to produce the hybrid progeny (F1). During the inbreeding process in corn, the vigor of the lines decreases. Vigor is restored when two unrelated inbred lines are crossed to produce the hybrid progeny (F1). An important consequence of the homozygosity and homogeneity of the inbred lines is that the hybrid between any two inbreds will always be the same. Once the inbreds that give a superior hybrid have been identified, the hybrid seed can be reproduced indefinitely as long as the homogeneity of the inbred parents is maintained.
A single cross hybrid is produced when two inbred lines are crossed to produce the F1 progeny. A double cross hybrid is produced from four inbred lines crossed in pairs (A×B and C×D) and then the two F1 hybrids are crossed again (A×B)×(C×D). Much of the hybrid vigor exhibited by F1 hybrids is lost in the next generation (F2). Consequently, seed from hybrid varieties is not used for planting stock.
Corn is an important and valuable field crop. Thus, a continuing goal of plant breeders is to develop consistent performing, high-yielding corn hybrids that are agronomically sound based on stable inbred lines. The reasons for this goal are obvious: to maximize the amount of grain produced with the inputs used and minimize susceptibility of the crop to environmental stresses. To accomplish this goal, the corn breeder must select and develop superior inbred parental lines for producing hybrids. This requires identification and selection of genetically unique individuals which in a segregating population occur as the result of a combination of crossover events plus the independent assortment of specific combinations of alleles at many gene loci which results in specific genotypes. Based on the number of segregating genes, the frequency of occurrence of an individual with a specific genotype is less than 1 in 10,000. Thus, even if the entire genotype of the parents has been characterized and the desired genotype is known, only a few, if any, individuals having the desired genotype may be found in a large F2 or S1 population. Typically, however, the genotype of neither the parents nor the desired genotype is known in any detail. An agronomically acceptable F1 hybrid will come from a cross between two superior inbred parental lines. There is no assurance that either of these parental lines will produce a superior hybrid when crossed with a different inbred parent line. Thus, the selection or combination of the two parental inbreds provides a unique hybrid that demonstrates characteristics and performance levels that differ from that obtained when either of the parents is crossed with a different inbred parent line.
Once the superior combination of two parental lines is determined by the testing and selection of the F1 hybrid, that F1 hybrid and the performance traits and characteristics of the hybrid can be indefinitely reproduced so long as the parental inbreds are maintained in their homozygosity and the quality and production procedures are accomplished to the purity standards determined by the seed industry regulation.
This evaluation has been so far performed separately for grain yield and moisture through use of a univariate mixed model analysis approach. The results are presented as a predicted value, generally referred to as a Best Linear Unbiased Prediction (BLUP). Along with the BLUP values, the accuracy of prediction can be calculated for each of the BLUP values. Accuracy is a measure that indicates how well the predicted values correlate with the “true” genetic values and can take on any value between 0 and 1. The closer the accuracy is to 1, the closer the predicted genetic value is to the true genetic value.
It is noteworthy that phenotypic measurements of inbred maize lines are rarely used for genetic evaluations in the seed industry; rather, records of hybrid (offspring) lines are normally used to draw inferences about the parent lines.
Wisser et al. (2011), Proc. Natl. Acad. Sci. USA 108(18):7339-44, used data recorded directly on inbred lines to study the genetics of multiple disease resistance in inbred maize lines. The objective of the study was to draw inferences on multiple disease resistance traits through variance component estimation and to test the hypothesis that markers are associated with multiple disease resistance traits. Wisser's method was based on a multi-variate mixed model; however his model differs in several aspects from the model disclosed herein. First, Wisser's inbred lines were not separated into male and female lines. Second, the relationship matrix used was constructed for all the lines in the study. Third, Wisser incorporated a subpopulation effect in his model as a fixed effect. Fourth, because the analysis was based on inbred data, specific combining ability (SCA), which must be derived from hybrid offspring produced from a specific male and female parental cross, could not be calculated.
In summary, although the two approaches are based on a multivariate mixed model approach, they differ in the components, the type of data to be analyzed and the final application of the results.